### A Special Issue of Mathematical Thinking and Learning

### A Special Issue of Mathematical Thinking and Learning

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The purpose of this special issue is to present several research perspectives on learning trajectories with the intention of encouraging the broader community to reflect on, better define, adopt, adapt, or challenge the concept. The issue begins by briefly introducing learning trajectories. The remaining articles provide elaboration, examples, and discussion of the construct. They purposefully are intended to be illustrative, exploratory, and provocative with regard to learning trajectories construct; they are not a set of verification studies.

**Volume 6, Number 2, 2004 **

**Contents: D.H. Clements, J. Sarama,** Learning Trajectories in Mathematics Education. **M. Simon, R. Tzur,** Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory. **K. Gravemeijer,** Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education. **L.P. Steffe,** On the Construction of Learning Trajectories of Children: The Case of Commensurate Fractions. **D.H. Clements, D.C. Wilson, J. Sarama,** Young Children's Composition of Geometric Figures: A Learning Trajectory. **M.T. Battista,** Applying Cognition-Based Assessment to Elementary School Students' Development of Understanding of Area and Volume Measurement. **R. Lesh, C. Yoon,** Evolving Communities of Mind--Where Development Involves Several Interacting and Simultaneously Development Strands. **A.J. Baroody, M. Cibulskis, M-L. Lai, X. Li,** Comments on the Use of Learning Trajectories in Curriculum Development and Research.

The purpose of this special issue is to present several research perspectives on learning trajectories with the intention of encouraging the broader community to reflect on, better define, adopt, adapt, or challenge the concept. The issue begins by briefly introducing learning trajectories. The remaining articles provide elaboration, examples, and discussion of the construct. They purposefully are intended to be illustrative, exploratory, and provocative with regard to learning trajectories construct; they are not a set of verification studies.

**Volume 6, Number 2, 2004 **

**Contents: D.H. Clements, J. Sarama,** Learning Trajectories in Mathematics Education. **M. Simon, R. Tzur,** Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory. **K. Gravemeijer,** Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education. **L.P. Steffe,** On the Construction of Learning Trajectories of Children: The Case of Commensurate Fractions. **D.H. Clements, D.C. Wilson, J. Sarama,** Young Children's Composition of Geometric Figures: A Learning Trajectory. **M.T. Battista,** Applying Cognition-Based Assessment to Elementary School Students' Development of Understanding of Area and Volume Measurement. **R. Lesh, C. Yoon,** Evolving Communities of Mind--Where Development Involves Several Interacting and Simultaneously Development Strands. **A.J. Baroody, M. Cibulskis, M-L. Lai, X. Li,** Comments on the Use of Learning Trajectories in Curriculum Development and Research.

The purpose of this special issue is to present several research perspectives on learning trajectories with the intention of encouraging the broader community to reflect on, better define, adopt, adapt, or challenge the concept. The issue begins by briefly introducing learning trajectories. The remaining articles provide elaboration, examples, and discussion of the construct. They purposefully are intended to be illustrative, exploratory, and provocative with regard to learning trajectories construct; they are not a set of verification studies.

**Volume 6, Number 2, 2004 **

**Contents: D.H. Clements, J. Sarama,** Learning Trajectories in Mathematics Education. **M. Simon, R. Tzur,** Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory. **K. Gravemeijer,** Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education. **L.P. Steffe,** On the Construction of Learning Trajectories of Children: The Case of Commensurate Fractions. **D.H. Clements, D.C. Wilson, J. Sarama,** Young Children's Composition of Geometric Figures: A Learning Trajectory. **M.T. Battista,** Applying Cognition-Based Assessment to Elementary School Students' Development of Understanding of Area and Volume Measurement. **R. Lesh, C. Yoon,** Evolving Communities of Mind--Where Development Involves Several Interacting and Simultaneously Development Strands. **A.J. Baroody, M. Cibulskis, M-L. Lai, X. Li,** Comments on the Use of Learning Trajectories in Curriculum Development and Research.

**Volume 6, Number 2, 2004 **

**Contents: D.H. Clements, J. Sarama,** Learning Trajectories in Mathematics Education. **M. Simon, R. Tzur,** Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory. **K. Gravemeijer,** Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education. **L.P. Steffe,** On the Construction of Learning Trajectories of Children: The Case of Commensurate Fractions. **D.H. Clements, D.C. Wilson, J. Sarama,** Young Children's Composition of Geometric Figures: A Learning Trajectory. **M.T. Battista,** Applying Cognition-Based Assessment to Elementary School Students' Development of Understanding of Area and Volume Measurement. **R. Lesh, C. Yoon,** Evolving Communities of Mind--Where Development Involves Several Interacting and Simultaneously Development Strands. **A.J. Baroody, M. Cibulskis, M-L. Lai, X. Li,** Comments on the Use of Learning Trajectories in Curriculum Development and Research.

**Volume 6, Number 2, 2004 **

**Contents: D.H. Clements, J. Sarama,** Learning Trajectories in Mathematics Education. **M. Simon, R. Tzur,** Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory. **K. Gravemeijer,** Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education. **L.P. Steffe,** On the Construction of Learning Trajectories of Children: The Case of Commensurate Fractions. **D.H. Clements, D.C. Wilson, J. Sarama,** Young Children's Composition of Geometric Figures: A Learning Trajectory. **M.T. Battista,** Applying Cognition-Based Assessment to Elementary School Students' Development of Understanding of Area and Volume Measurement. **R. Lesh, C. Yoon,** Evolving Communities of Mind--Where Development Involves Several Interacting and Simultaneously Development Strands. **A.J. Baroody, M. Cibulskis, M-L. Lai, X. Li,** Comments on the Use of Learning Trajectories in Curriculum Development and Research.

**Volume 6, Number 2, 2004 **

**Contents: D.H. Clements, J. Sarama,** Learning Trajectories in Mathematics Education. **M. Simon, R. Tzur,** Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory. **K. Gravemeijer,** Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education. **L.P. Steffe,** On the Construction of Learning Trajectories of Children: The Case of Commensurate Fractions. **D.H. Clements, D.C. Wilson, J. Sarama,** Young Children's Composition of Geometric Figures: A Learning Trajectory. **M.T. Battista,** Applying Cognition-Based Assessment to Elementary School Students' Development of Understanding of Area and Volume Measurement. **R. Lesh, C. Yoon,** Evolving Communities of Mind--Where Development Involves Several Interacting and Simultaneously Development Strands. **A.J. Baroody, M. Cibulskis, M-L. Lai, X. Li,** Comments on the Use of Learning Trajectories in Curriculum Development and Research.